What are the solutions to the equation x^2+3/2 x+9/16 =3 ?

The solutions to the equation x^2+3/2 x+9/16 =3 are x=(-3+4sqrt(3))/4 ,x=-(3+4sqrt(3))/4

Find the zeros of x^2+3/2 x+9/16 =3

The zeros of x^2+3/2 x+9/16 =3 are x=(-3+4sqrt(3))/4 ,x=-(3+4sqrt(3))/4

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x^{2} + \frac{3}{2} x + \frac{9}{16} = 3

x = \frac{- 3 + 4 3}{4}, x = - \frac{3 + 4 3}{4}

Decimal Notation

x = 0.98205 \dots, x = - 2.48205 \dots

Solution steps

x^{2} + \frac{3}{2} x + \frac{9}{16} = 3

Find Least Common Multiplier of

2, 16 : 16

Multiply by LCM=

16

x^{2} \cdot 16 + \frac{3}{2} x \cdot 16 + \frac{9}{16} \cdot 16 = 3 \cdot 16

Simplify

16 x^{2} + 24 x + 9 = 48

Move

48

to the left side

16 x^{2} + 24 x - 39 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 24 \pm 2 4 ^{2} - 4 \cdot 16 ( - 39 )}{2 \cdot 16}

2 4^{2} - 4 \cdot 16 (- 39) = 323

x_{1, 2} = \frac{- 24 \pm 32 3}{2 \cdot 16}

Separate the solutions

x_{1} = \frac{- 24 + 32 3}{2 \cdot 16}, x_{2} = \frac{- 24 - 32 3}{2 \cdot 16}

x = \frac{- 24 + 32 3}{2 \cdot 16} : \frac{- 3 + 4 3}{4}

x = \frac{- 24 - 32 3}{2 \cdot 16} : - \frac{3 + 4 3}{4}

The solutions to the quadratic equation are:

x = \frac{- 3 + 4 3}{4}, x = - \frac{3 + 4 3}{4}

2^{2} + 7^{2} = c^{2}

(2 x - 1)^{2} = 4.5 x

4^{2} + 8^{2} = x^{2}

z^{2} - 2 z - 3 = 0

9 x^{2} + 9 = 0

What are the solutions to the equation x^2+3/2 x+9/16 =3 ?
The solutions to the equation x^2+3/2 x+9/16 =3 are x=(-3+4sqrt(3))/4 ,x=-(3+4sqrt(3))/4
Find the zeros of x^2+3/2 x+9/16 =3
The zeros of x^2+3/2 x+9/16 =3 are x=(-3+4sqrt(3))/4 ,x=-(3+4sqrt(3))/4